Abstract We consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.

中文翻译：

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开放周期波导缺陷的分解和单调性方法

摘要 我们考虑逆散射问题，从近场数据重建上半空间周期性无限介质中的缺陷。这篇论文有两个贡献。首先，我们提到早期论文 [A. Lechleiter，分解方法与传输特征值无关，逆问题。Imaging 3 2009, 1, 123–138] 并给出正确的一个。其次，结合分解法和单调法，给出了两种未知缺陷的重建算法。我们还给出了基于前一种算法的数值例子。